Maharashtra PSC – Reasoning Ability
Topic: Seating Arrangement
Goal: Learn how to decode seating arrangements quickly and accurately.
Approach: Understand the language of the problem, translate it into a diagram, and apply inference rules.
1. Simple Explanation
A seating arrangement problem gives you a set of people and a set of seats (often in a row or a circle).
You are provided with a list of relative clues such as:
- “A sits to the left of B”
- “C is two seats right of D”
- “E is between X and Y”
Your task is to determine the exact order or position of each person.
The key is to convert the verbal clues into a visual map (a line or circular diagram) and then fill it in step by step.
2. Key Points (The “Rule‑book”)
| # | What to Watch For | How to Handle It |
|---|---|---|
| 1 | Direction – “left”, “right”, “clockwise”, “counter‑clockwise” | In a row: left ↔ earlier index; right ↔ later index. In a circle: clockwise → +1, counter‑clockwise → –1. |
| 2 | Distance – “next to”, “two seats after”, “between” | Count the number of seats, excluding the reference person. |
| 3 | Relative positions – “A is between B and C” | B – A – C or C – A – B. |
| 4 | Fixed positions – “A sits at the far left / right / middle” | Place A first; it becomes a reference point. |
| 5 | Opposite / Across (in a circle) | Opposite means 180° apart; in a 10‑seat circle, seat i is opposite seat i+5. |
| 6 | Simultaneous constraints | Use back‑tracking: try one hypothesis, see if contradictions appear. |
| 7 | Symmetry | If “two people are opposite each other” and only one pair is specified, the order of the pair can be swapped. |
| 8 | Unnecessary information | Ignore clues that don’t affect the final order. |
| 9 | Check consistency | After filling the diagram, re‑read all clues to ensure no conflict. |
| 10 | Time‑saving tip | Start with the most restrictive clue (e.g., fixed position or “exactly two seats apart”). |
3. Worked Example
Problem Statement
10 people – A, B, C, D, E, F, G, H, I, J – are seated in a row.
The following information is known:
- B sits to the left of E.
- C sits exactly two seats to the right of B.
- G is between E and I.
- H sits at the far right.
- J sits immediately to the right of F.
- D sits between A and C.
- E sits at the third position from the left.
- I sits to the left of H.
Question: What is the seating order from left to right?
Step‑by‑Step Solution
| Step | Reasoning | Diagram (row of 10) |
|---|---|---|
| 1 | From (7) E is at position 3. | - - E - - - - - - - |
| 2 | (1) B is left of E, so B is at position 1 or 2. | B? - E - - - - - - - |
| 3 | (2) C is two seats right of B. If B=1 → C=4. If B=2 → C=5. Keep both possibilities. | B? - E - - - - - - - (C at 4 or 5) |
| 4 | (4) H is at far right → position 10. | B? - E - - - - - - H |
| 5 | (8) I left of H → I somewhere in 1‑9. | |
| 6 | (3) G between E and I. So pattern: E – G – I or I – G – E. Since E is at 3, possibilities: (E=3, G=4, I=5) or (I=4, G=5, E=3). | |
| 7 | Combine with Step 3: |
- If C=4, then G cannot be at 4 ⇒ invalid.
- If C=5, then G could be 4 and I=5? Wait C=5 already, cannot.
Hence C cannot be 5. So C=4. |B? - E C - - - - - H| | 8 | From (3) with C=4, the only arrangement isI – G – E? Wait: G must be between E and I. E at 3, so G at 4? But C already at 4. Contradiction. So our assumption wrong. Let's try alternative: maybe G between I and E: I at 4, G at 5, E at 3. That works: I=4, G=5, E=3. |B? - E I G - - - - H| | 9 | Now we have B at position 1 or 2. C is two seats right of B. If B=1 → C=3? But E already at 3. So B cannot be 1. Therefore B=2, C=4? Wait C=4 already occupied by I. Contradiction. Let's re‑evaluate. | | 10 | Realize we mis‑interpreted (3). “G is between E and I” means G is exactly between them, not necessarily adjacent. So pattern: E – G – I or I – G – E with *one seat between